To ensure very precise imaging of the mask structures on the wafer, a projection lens with the fewest possible wavefront aberrations is desired. Projection lenses are therefore equipped with manipulators which render it possible to correct wavefront aberrations by changing the state of individual optical elements of the projection lens. Examples of such a state change include a change in position in one or more of the six rigid body degrees of freedom of the relevant optical element, an application of heat and/or coldness to the optical element, and a deformation of the optical element. Usually, the aberration characteristic of the projection lens is measured at regular intervals and, if desired, changes in the aberration characteristic are determined between the individual measurements by simulation. Thus, for example, lens-element heating effects can be taken into account in calculations. The terms “lens heating”, “lens-element warming”, “mirror heating” and “mirror warming” are also used synonymously for “lens-element heating”. The manipulator changes to be carried out to correct the aberration characteristic are calculated using a travel generating optimization algorithm, which is also referred to as “manipulator changing model”.
“Travel” is understood to mean a change in a state variable of an optical element, effected via manipulator actuation, for the purpose of changing the optical effects thereof. Such travel defined by changing a state variable of the optical element is specified by intended change variables of the manipulator. By way of example, the manipulation can consist of a displacement of the optical element in a specific direction, but also, for example, of a local or two-dimensional loading of the optical element with heat, coldness, forces, light of a specific wavelength or currents. By way of example, the intended change variable can, in the case of a displacement, define a path length to be travelled or an angular range to be travelled.
The desire for continuous miniaturization of the structures to be imaged and for increasing the throughput lead to the situation where the aberration characteristic cannot, in general, be corrected sufficiently satisfactorily in a conventional manner by manipulators, neither during operation nor over the service life of a projection exposure apparatus. In this case, “sufficiently satisfactorily” is understood to mean that the uncorrected residual aberration characteristic leads to a sufficient imaging quality for a multiplicity of usage configurations. Here, a usage configuration should be understood to mean a combination of a mask with an illumination setting used for imaging the same.
It was found to be desirable to set the residual aberration characteristic in view of the processed usage configurations so that important structures, in particular so-called core-region structures (described in more detail below), are imaged very precisely and so that the residual structures, i.e. the peripheral structures, are imaged less precisely but still sufficiently precisely. This is possible, among other reasons, because core-region structures and peripheral structures scan different regions of the wavefronts and the peripheral structures pose significantly lower demands on the scanned wavefront region.
It is known to use travel generating optimization algorithms which usually solve unrestricted quadratic optimization problems in regularized fashion, usually via matrix multiplication by a single preceding calculation of the inverse. To regularize so-called “ill-posed problems”, use is made in particular of singular value decomposition with singular-value cut-off or Tikhonov regularization. Details are disclosed in, for example, “Iterative Methods for III-Posed Problems: An Introduction,” Inverse and III-Posed Problems, B. Bakushinsky, Mihail Y. Kokurin and Alexandra Smirnova, De Gruyter, 2010, chapters 4 and 5, pages 23-43. Here, the respective user configuration can, as a matter of principle, not be taken or not be sufficiently taken into account.